To my ear the song is in the key of F (major).
So the main progression is:
F (I), Am (iii), Eb (I b7), Bb (IV)
[tonic => mediant, then the Eb (dominant of the subdominant = I b7) resolves to Bb (the subdominant)]
The break (from 02:26) is based on Gm (ii) with the bass fallin in half steps: g...